"A respiratory therapy class consist of 3 men and 57 women. What fraction of the students in the class are men? Express your answer as a fraction reduced to its lowest terms."

I have tried to solve the question however my answer did not match to correct answer which is found on my book. The thing is, the bok doesnt show how to solve the problem. It just gives you the answer. Here is what I did: 3/57 and multiplied both by 100 = 300/5700 and the I reduced it to its lowest terms by dividing 300 to both 300/5700. So my answer is 1/19. That is not the answer on the book though. pls help.